So that's what Plato's trying to do That's the isomorphism between these two spheres that he's trying to demasculinize.

这正是柏拉图所努力实现的目标——他试图消除这两个领域的同构关系，使其不再具有男性化的特征。

When you have a correspondence where this remains true for all products, it's called an " isomorphism" , which is maybe the most important idea in group theory.

当一个对应关系对于所有保持为真时，这被称为“同构” ， 这可能是群论中最重要的概念。

Isomorphic because we believe there is an isomorphism, a fundamental symmetry, that we can create between the biological world and the world of information science, machine learning and AI.

同构是因为我们认为生物世与信息科学、机器学习和人工智能世存在着一种同构关系，一种基本的对称性。

Vaida's treatment of the verbal morphology involves a tiny handful of intriguing isomorphisms, surrounded by an impenetrable sea of assumptions and highly controversial internal reconstructions that create an illusion of systemic reconstruction where there really is none.

Vaida 对词语形态学的处理涉及极少数有趣的同构，而这些同构周围则充满了难以理解的假设和极具争议的内部重建， 造成了一种系统重建的假象， 但实际上并不存在这种重建。

This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.

这种立方体旋转与四个对象排列的同构关系有点微妙，但对于你们中好奇的人来说， 你们可能会喜欢花点时思考一下立方体的旋转是如何对其四条对角线进行排列的。

But now you're in a position to ask that question in a more sophisticated way: What are all the groups up to isomorphism, which is to say we consider two groups to be the same if there's an isomorphism between them.

但现在你可以用更成熟的方式提出这个问题：在同构的意义上，所有的群有哪些？ 也就是说，如果我们能在两个群找到同构关系， 我们就认为这两个群是相同的。